12a
0515
(K12a
0515
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 1 10 4 12 5 6
Solving Sequence
5,9
4 10 8
3,12
11 6 1 7 2
c
4
c
9
c
8
c
3
c
11
c
5
c
12
c
7
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
33
+ u
32
+ ··· + 4a + 1, u
34
+ 9u
32
+ ··· + 2u + 1i
I
u
2
= h−3.29206 × 10
15
u
57
+ 7.29251 × 10
15
u
56
+ ··· + 6.43771 × 10
15
b + 1.37987 × 10
16
, u
57
− u
56
+ ··· + a − 8,
u
58
− u
57
+ ··· − 8u + 1i
I
u
3
= hb + u, a
2
+ 2au − a − u, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 96 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hb − u, u
33
+ u
32
+ · · · + 4a + 1, u
34
+ 9u
32
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
−u
u
3
+ u
a
8
=
−u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
12
=
−
1
4
u
33
−
1
4
u
32
+ ··· −
11
4
u −
1
4
u
a
11
=
−
1
4
u
33
−
1
4
u
32
+ ··· −
7
4
u −
1
4
u
a
6
=
−
1
4
u
33
+
1
4
u
32
+ ··· +
1
4
u +
5
4
u
2
a
1
=
−
1
4
u
33
−
1
4
u
32
+ ··· −
7
4
u −
1
4
u
5
+ u
3
+ u
a
7
=
7
4
u
33
+
5
4
u
32
+ ··· +
23
4
u +
7
4
−
1
4
u
33
−
1
4
u
32
+ ··· +
1
4
u −
1
4
a
2
=
−
1
2
u
33
−
1
2
u
32
+ ··· −
7
2
u −
1
2
−
1
4
u
33
−
1
4
u
32
+ ··· +
1
4
u −
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −6u
33
+u
32
−53u
31
+5u
30
−234u
29
+9u
28
−642u
27
−13u
26
−1183u
25
−104u
24
−1454u
23
−
276u
22
−1067u
21
−433u
20
−162u
19
−423u
18
+569u
17
−178u
16
+658u
15
+134u
14
+288u
13
+
280u
12
−22u
11
+ 188u
10
−106u
9
+ 30u
8
−52u
7
−40u
6
−19u
5
−35u
4
−2u
3
−11u
2
−5u −4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 15u
33
+ ··· − 3u + 4
c
2
, c
6
u
34
− 3u
33
+ ··· − 3u + 2
c
3
, c
12
u
34
+ 3u
33
+ ··· + 48u + 32
c
4
, c
5
, c
9
c
11
u
34
+ 9u
32
+ ··· + 2u + 1
c
7
u
34
− 9u
33
+ ··· − 13u + 6
c
8
, c
10
u
34
− 18u
33
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 9y
33
+ ··· − 225y + 16
c
2
, c
6
y
34
− 15y
33
+ ··· + 3y + 4
c
3
, c
12
y
34
− 29y
33
+ ··· + 12544y + 1024
c
4
, c
5
, c
9
c
11
y
34
+ 18y
33
+ ··· + 4y + 1
c
7
y
34
− 3y
33
+ ··· + 563y + 36
c
8
, c
10
y
34
+ 2y
33
+ ··· − 12y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325102 + 0.931137I
a = 3.02864 − 0.12001I
b = −0.325102 + 0.931137I
2.90695 + 0.12402I 1.68955 − 3.89611I
u = −0.325102 − 0.931137I
a = 3.02864 + 0.12001I
b = −0.325102 − 0.931137I
2.90695 − 0.12402I 1.68955 + 3.89611I
u = 0.379532 + 0.974939I
a = −2.71723 + 0.31509I
b = 0.379532 + 0.974939I
3.60419 − 5.09535I 3.52400 + 9.16731I
u = 0.379532 − 0.974939I
a = −2.71723 − 0.31509I
b = 0.379532 − 0.974939I
3.60419 + 5.09535I 3.52400 − 9.16731I
u = −0.545074 + 0.928759I
a = 1.93949 + 0.24437I
b = −0.545074 + 0.928759I
−2.30189 + 4.06636I −5.42219 − 5.57604I
u = −0.545074 − 0.928759I
a = 1.93949 − 0.24437I
b = −0.545074 − 0.928759I
−2.30189 − 4.06636I −5.42219 + 5.57604I
u = 0.578615 + 0.697678I
a = −1.53750 − 0.18162I
b = 0.578615 + 0.697678I
−3.69260 − 4.93095I −7.79856 + 7.85932I
u = 0.578615 − 0.697678I
a = −1.53750 + 0.18162I
b = 0.578615 − 0.697678I
−3.69260 + 4.93095I −7.79856 − 7.85932I
u = 0.512199 + 1.009370I
a = −2.07083 + 0.50301I
b = 0.512199 + 1.009370I
1.80817 − 6.75607I 1.65159 + 7.76027I
u = 0.512199 − 1.009370I
a = −2.07083 − 0.50301I
b = 0.512199 − 1.009370I
1.80817 + 6.75607I 1.65159 − 7.76027I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832688 + 0.098135I
a = 0.991071 − 0.020370I
b = −0.832688 + 0.098135I
1.75556 − 6.53805I −3.65158 + 4.76595I
u = −0.832688 − 0.098135I
a = 0.991071 + 0.020370I
b = −0.832688 − 0.098135I
1.75556 + 6.53805I −3.65158 − 4.76595I
u = −0.558467 + 1.025310I
a = 1.91347 + 0.53985I
b = −0.558467 + 1.025310I
−0.53806 + 11.42870I −2.07055 − 11.36920I
u = −0.558467 − 1.025310I
a = 1.91347 − 0.53985I
b = −0.558467 − 1.025310I
−0.53806 − 11.42870I −2.07055 + 11.36920I
u = 0.818774 + 0.055314I
a = −0.982841 − 0.012957I
b = 0.818774 + 0.055314I
3.55824 + 1.37935I −0.788316 − 0.189329I
u = 0.818774 − 0.055314I
a = −0.982841 + 0.012957I
b = 0.818774 − 0.055314I
3.55824 − 1.37935I −0.788316 + 0.189329I
u = 0.599904 + 0.533096I
a = −1.259450 − 0.242292I
b = 0.599904 + 0.533096I
−3.45372 + 2.17892I −8.19265 − 0.78850I
u = 0.599904 − 0.533096I
a = −1.259450 + 0.242292I
b = 0.599904 − 0.533096I
−3.45372 − 2.17892I −8.19265 + 0.78850I
u = −0.463929 + 0.613637I
a = 1.43733 − 0.48756I
b = −0.463929 + 0.613637I
−0.77203 + 1.45962I −3.64985 − 4.39900I
u = −0.463929 − 0.613637I
a = 1.43733 + 0.48756I
b = −0.463929 − 0.613637I
−0.77203 − 1.45962I −3.64985 + 4.39900I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.058121 + 0.707802I
a = 0.67473 − 2.70722I
b = −0.058121 + 0.707802I
1.89006 + 2.33981I −2.06348 − 4.83250I
u = −0.058121 − 0.707802I
a = 0.67473 + 2.70722I
b = −0.058121 − 0.707802I
1.89006 − 2.33981I −2.06348 + 4.83250I
u = 0.455016 + 1.223690I
a = −1.85829 + 1.30176I
b = 0.455016 + 1.223690I
9.41425 − 2.26828I 3.84198 + 1.66099I
u = 0.455016 − 1.223690I
a = −1.85829 − 1.30176I
b = 0.455016 − 1.223690I
9.41425 + 2.26828I 3.84198 − 1.66099I
u = 0.502151 + 1.208700I
a = −1.79600 + 1.13625I
b = 0.502151 + 1.208700I
4.92319 − 8.99452I −0.64598 + 6.18414I
u = 0.502151 − 1.208700I
a = −1.79600 − 1.13625I
b = 0.502151 − 1.208700I
4.92319 + 8.99452I −0.64598 − 6.18414I
u = −0.471167 + 1.229680I
a = 1.80562 + 1.26527I
b = −0.471167 + 1.229680I
10.96840 + 7.70284I 5.88314 − 6.31292I
u = −0.471167 − 1.229680I
a = 1.80562 − 1.26527I
b = −0.471167 − 1.229680I
10.96840 − 7.70284I 5.88314 + 6.31292I
u = −0.505650 + 1.237960I
a = 1.71513 + 1.18708I
b = −0.505650 + 1.237960I
10.4811 + 11.0888I 5.24755 − 6.29761I
u = −0.505650 − 1.237960I
a = 1.71513 − 1.18708I
b = −0.505650 − 1.237960I
10.4811 − 11.0888I 5.24755 + 6.29761I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517793 + 1.240450I
a = −1.68661 + 1.16146I
b = 0.517793 + 1.240450I
8.5255 − 16.4951I 2.48715 + 10.53495I
u = 0.517793 − 1.240450I
a = −1.68661 − 1.16146I
b = 0.517793 − 1.240450I
8.5255 + 16.4951I 2.48715 − 10.53495I
u = −0.603784 + 0.120649I
a = 0.903265 − 0.081259I
b = −0.603784 + 0.120649I
−1.374120 + 0.056938I −8.04181 − 0.45321I
u = −0.603784 − 0.120649I
a = 0.903265 + 0.081259I
b = −0.603784 − 0.120649I
−1.374120 − 0.056938I −8.04181 + 0.45321I
8
II. I
u
2
= h−3.29 × 10
15
u
57
+ 7.29 × 10
15
u
56
+ · · · + 6.44 × 10
15
b + 1.38 ×
10
16
, u
57
− u
56
+ · · · + a − 8, u
58
− u
57
+ · · · − 8u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
−u
u
3
+ u
a
8
=
−u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
12
=
−u
57
+ u
56
+ ··· − 24u + 8
0.511371u
57
− 1.13278u
56
+ ··· + 9.35148u − 2.14342
a
11
=
−0.488629u
57
− 0.132779u
56
+ ··· − 14.6485u + 5.85658
0.511371u
57
− 1.13278u
56
+ ··· + 9.35148u − 2.14342
a
6
=
2.76482u
57
− 1.51842u
56
+ ··· + 35.9278u − 7.28447
0.621408u
57
+ 0.113621u
56
+ ··· − 1.94755u − 0.488629
a
1
=
−0.601427u
57
+ 0.507022u
56
+ ··· − 15.5095u + 5.87233
1.13360u
57
− 1.24375u
56
+ ··· + 12.9732u − 2.74908
a
7
=
−1.13256u
57
+ 0.211579u
56
+ ··· − 4.76871u − 1.87504
−2.01309u
57
+ 0.873239u
56
+ ··· − 17.7387u + 3.68030
a
2
=
−1.51241u
57
+ 1.43774u
56
+ ··· − 29.1091u + 8.72049
0.0761347u
57
− 0.931485u
56
+ ··· + 1.76325u − 1.13509
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
19080003654706928
6437714387382889
u
57
+
23944909507695016
6437714387382889
u
56
+···−
592292412509243776
6437714387382889
u+
107001468804774338
6437714387382889
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
29
+ 13u
28
+ ··· + 3u + 1)
2
c
2
, c
6
(u
29
+ u
28
+ ··· + u + 1)
2
c
3
, c
12
(u
29
− u
28
+ ··· − 7u + 1)
2
c
4
, c
5
, c
9
c
11
u
58
− u
57
+ ··· − 8u + 1
c
7
(u
29
+ 3u
28
+ ··· − u − 1)
2
c
8
, c
10
u
58
− 35u
57
+ ··· + 16u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ 7y
28
+ ··· − 17y −1)
2
c
2
, c
6
(y
29
− 13y
28
+ ··· + 3y −1)
2
c
3
, c
12
(y
29
− 29y
28
+ ··· + 19y −1)
2
c
4
, c
5
, c
9
c
11
y
58
+ 35y
57
+ ··· − 16y + 1
c
7
(y
29
− y
28
+ ··· + 31y −1)
2
c
8
, c
10
y
58
− 25y
57
+ ··· − 84y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.451687 + 0.902213I
a = −0.443696 − 0.886253I
b = 0.596507 + 0.373464I
0.04989 + 2.39104I −1.72606 − 3.37022I
u = −0.451687 − 0.902213I
a = −0.443696 + 0.886253I
b = 0.596507 − 0.373464I
0.04989 − 2.39104I −1.72606 + 3.37022I
u = −0.355580 + 0.921167I
a = −0.364702 − 0.944801I
b = −0.148977 − 1.212380I
2.70580 + 4.33232I 0.72516 − 7.80862I
u = −0.355580 − 0.921167I
a = −0.364702 + 0.944801I
b = −0.148977 + 1.212380I
2.70580 − 4.33232I 0.72516 + 7.80862I
u = −0.136657 + 0.974285I
a = −0.141188 − 1.006590I
b = 0.241604 + 0.089146I
1.78353 + 2.08825I 0.67041 − 4.01921I
u = −0.136657 − 0.974285I
a = −0.141188 + 1.006590I
b = 0.241604 − 0.089146I
1.78353 − 2.08825I 0.67041 + 4.01921I
u = 0.537066 + 0.794398I
a = 0.584080 − 0.863939I
b = −0.613212 + 0.531150I
−3.41971 + 0.47843I −8.05109 − 0.53373I
u = 0.537066 − 0.794398I
a = 0.584080 + 0.863939I
b = −0.613212 − 0.531150I
−3.41971 − 0.47843I −8.05109 + 0.53373I
u = 0.274360 + 1.012700I
a = 0.249230 − 0.919941I
b = 0.193653 − 1.136220I
4.30269 − 0.27837I 6.00481 + 1.83311I
u = 0.274360 − 1.012700I
a = 0.249230 + 0.919941I
b = 0.193653 + 1.136220I
4.30269 + 0.27837I 6.00481 − 1.83311I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533835 + 0.932703I
a = 0.462229 − 0.807594I
b = −0.698762 + 0.398387I
−2.32632 − 6.65351I −5.43843 + 7.12693I
u = 0.533835 − 0.932703I
a = 0.462229 + 0.807594I
b = −0.698762 − 0.398387I
−2.32632 + 6.65351I −5.43843 − 7.12693I
u = 0.897586 + 0.099606I
a = 1.100550 − 0.122128I
b = −0.501810 + 1.214960I
5.07686 + 11.39320I −0.48604 − 7.74456I
u = 0.897586 − 0.099606I
a = 1.100550 + 0.122128I
b = −0.501810 − 1.214960I
5.07686 − 11.39320I −0.48604 + 7.74456I
u = −0.881384 + 0.080515I
a = −1.125190 − 0.102787I
b = 0.483040 + 1.216550I
6.99366 − 6.09123I 2.35632 + 3.37420I
u = −0.881384 − 0.080515I
a = −1.125190 + 0.102787I
b = 0.483040 − 1.216550I
6.99366 + 6.09123I 2.35632 − 3.37420I
u = 0.193653 + 1.136220I
a = 0.145769 − 0.855267I
b = 0.274360 − 1.012700I
4.30269 + 0.27837I 0
u = 0.193653 − 1.136220I
a = 0.145769 + 0.855267I
b = 0.274360 + 1.012700I
4.30269 − 0.27837I 0
u = −0.839368 + 0.022570I
a = −1.190510 − 0.032012I
b = 0.431178 + 1.224900I
7.36652 − 3.00599I 2.90218 + 3.08222I
u = −0.839368 − 0.022570I
a = −1.190510 + 0.032012I
b = 0.431178 − 1.224900I
7.36652 + 3.00599I 2.90218 − 3.08222I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820017 + 0.108595I
a = 1.198470 − 0.158714I
b = −0.464569 + 1.169820I
1.65953 + 4.16530I −3.77294 − 3.16142I
u = 0.820017 − 0.108595I
a = 1.198470 + 0.158714I
b = −0.464569 − 1.169820I
1.65953 − 4.16530I −3.77294 + 3.16142I
u = −0.031586 + 1.172780I
a = −0.022949 − 0.852059I
b = −0.201393 − 0.714310I
1.84033 + 1.50061I 0
u = −0.031586 − 1.172780I
a = −0.022949 + 0.852059I
b = −0.201393 + 0.714310I
1.84033 − 1.50061I 0
u = 0.819192 + 0.008052I
a = 1.220600 − 0.011997I
b = −0.405561 − 1.230110I
5.76313 + 2.27350I 0.56508 − 1.80235I
u = 0.819192 − 0.008052I
a = 1.220600 + 0.011997I
b = −0.405561 + 1.230110I
5.76313 − 2.27350I 0.56508 + 1.80235I
u = −0.613212 + 0.531150I
a = −0.931721 − 0.807036I
b = 0.537066 + 0.794398I
−3.41971 + 0.47843I −8.05109 − 0.53373I
u = −0.613212 − 0.531150I
a = −0.931721 + 0.807036I
b = 0.537066 − 0.794398I
−3.41971 − 0.47843I −8.05109 + 0.53373I
u = −0.698762 + 0.398387I
a = −1.080040 − 0.615764I
b = 0.533835 + 0.932703I
−2.32632 − 6.65351I −5.43843 + 7.12693I
u = −0.698762 − 0.398387I
a = −1.080040 + 0.615764I
b = 0.533835 − 0.932703I
−2.32632 + 6.65351I −5.43843 − 7.12693I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148977 + 1.212380I
a = −0.099847 − 0.812557I
b = −0.355580 − 0.921167I
2.70580 − 4.33232I 0
u = −0.148977 − 1.212380I
a = −0.099847 + 0.812557I
b = −0.355580 + 0.921167I
2.70580 + 4.33232I 0
u = −0.201393 + 0.714310I
a = −0.365639 − 1.296860I
b = −0.031586 − 1.172780I
1.84033 − 1.50061I −3.01904 + 0.45145I
u = −0.201393 − 0.714310I
a = −0.365639 + 1.296860I
b = −0.031586 + 1.172780I
1.84033 + 1.50061I −3.01904 − 0.45145I
u = −0.464569 + 1.169820I
a = −0.293234 − 0.738384I
b = 0.820017 + 0.108595I
1.65953 + 4.16530I 0
u = −0.464569 − 1.169820I
a = −0.293234 + 0.738384I
b = 0.820017 − 0.108595I
1.65953 − 4.16530I 0
u = 0.401017 + 1.217560I
a = 0.244038 − 0.740940I
b = 0.401017 − 1.217560I
5.63906 0
u = 0.401017 − 1.217560I
a = 0.244038 + 0.740940I
b = 0.401017 + 1.217560I
5.63906 0
u = −0.405561 + 1.230110I
a = −0.241745 − 0.733235I
b = 0.819192 − 0.008052I
5.76313 − 2.27350I 0
u = −0.405561 − 1.230110I
a = −0.241745 + 0.733235I
b = 0.819192 + 0.008052I
5.76313 + 2.27350I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.596507 + 0.373464I
a = 1.20434 − 0.75402I
b = −0.451687 + 0.902213I
0.04989 + 2.39104I −1.72606 − 3.37022I
u = 0.596507 − 0.373464I
a = 1.20434 + 0.75402I
b = −0.451687 − 0.902213I
0.04989 − 2.39104I −1.72606 + 3.37022I
u = 0.431178 + 1.224900I
a = 0.255695 − 0.726386I
b = −0.839368 + 0.022570I
7.36652 − 3.00599I 0
u = 0.431178 − 1.224900I
a = 0.255695 + 0.726386I
b = −0.839368 − 0.022570I
7.36652 + 3.00599I 0
u = 0.462658 + 1.222210I
a = 0.270900 − 0.715642I
b = 0.404660 − 1.277940I
9.35892 − 6.86231I 0
u = 0.462658 − 1.222210I
a = 0.270900 + 0.715642I
b = 0.404660 + 1.277940I
9.35892 + 6.86231I 0
u = 0.483040 + 1.216550I
a = 0.281933 − 0.710054I
b = −0.881384 + 0.080515I
6.99366 − 6.09123I 0
u = 0.483040 − 1.216550I
a = 0.281933 + 0.710054I
b = −0.881384 − 0.080515I
6.99366 + 6.09123I 0
u = −0.448712 + 1.234520I
a = −0.260066 − 0.715506I
b = −0.417116 − 1.264920I
11.13090 + 1.55857I 0
u = −0.448712 − 1.234520I
a = −0.260066 + 0.715506I
b = −0.417116 + 1.264920I
11.13090 − 1.55857I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501810 + 1.214960I
a = −0.290411 − 0.703128I
b = 0.897586 + 0.099606I
5.07686 + 11.39320I 0
u = −0.501810 − 1.214960I
a = −0.290411 + 0.703128I
b = 0.897586 − 0.099606I
5.07686 − 11.39320I 0
u = −0.417116 + 1.264920I
a = −0.235126 − 0.713028I
b = −0.448712 − 1.234520I
11.13090 − 1.55857I 0
u = −0.417116 − 1.264920I
a = −0.235126 + 0.713028I
b = −0.448712 + 1.234520I
11.13090 + 1.55857I 0
u = 0.404660 + 1.277940I
a = 0.225201 − 0.711199I
b = 0.462658 − 1.222210I
9.35892 + 6.86231I 0
u = 0.404660 − 1.277940I
a = 0.225201 + 0.711199I
b = 0.462658 + 1.222210I
9.35892 − 6.86231I 0
u = 0.241604 + 0.089146I
a = 3.64303 − 1.34418I
b = −0.136657 + 0.974285I
1.78353 + 2.08825I 0.67041 − 4.01921I
u = 0.241604 − 0.089146I
a = 3.64303 + 1.34418I
b = −0.136657 − 0.974285I
1.78353 − 2.08825I 0.67041 + 4.01921I
17
III. I
u
3
= hb + u, a
2
+ 2au − a − u, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
1
a
10
=
−u
0
a
8
=
u
u
a
3
=
1
1
a
12
=
a
−u
a
11
=
a − u
−u
a
6
=
−au
−1
a
1
=
a
−u
a
7
=
−au − a + u + 1
−a
a
2
=
2a + u
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 4u + 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
6
, c
7
u
4
− u
2
+ 1
c
3
, c
12
u
4
c
4
, c
5
, c
9
c
11
(u
2
+ 1)
2
c
8
, c
10
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
6
, c
7
(y
2
− y + 1)
2
c
3
, c
12
y
4
c
4
, c
5
, c
9
c
11
(y + 1)
4
c
8
, c
10
(y −1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 − 0.133975I
b = − 1.000000I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.000000I
a = 0.50000 − 1.86603I
b = − 1.000000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = 0.500000 + 0.133975I
b = 1.000000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = 0.50000 + 1.86603I
b = 1.000000I
3.28987 − 2.02988I 6.00000 + 3.46410I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
29
+ 13u
28
+ ··· + 3u + 1)
2
· (u
34
+ 15u
33
+ ··· − 3u + 4)
c
2
, c
6
(u
4
− u
2
+ 1)(u
29
+ u
28
+ ··· + u + 1)
2
(u
34
− 3u
33
+ ··· − 3u + 2)
c
3
, c
12
u
4
(u
29
− u
28
+ ··· − 7u + 1)
2
(u
34
+ 3u
33
+ ··· + 48u + 32)
c
4
, c
5
, c
9
c
11
((u
2
+ 1)
2
)(u
34
+ 9u
32
+ ··· + 2u + 1)(u
58
− u
57
+ ··· − 8u + 1)
c
7
(u
4
− u
2
+ 1)(u
29
+ 3u
28
+ ··· − u − 1)
2
(u
34
− 9u
33
+ ··· − 13u + 6)
c
8
, c
10
((u + 1)
4
)(u
34
− 18u
33
+ ··· − 4u + 1)(u
58
− 35u
57
+ ··· + 16u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
29
+ 7y
28
+ ··· − 17y −1)
2
· (y
34
+ 9y
33
+ ··· − 225y + 16)
c
2
, c
6
((y
2
− y + 1)
2
)(y
29
− 13y
28
+ ··· + 3y −1)
2
· (y
34
− 15y
33
+ ··· + 3y + 4)
c
3
, c
12
y
4
(y
29
− 29y
28
+ ··· + 19y −1)
2
· (y
34
− 29y
33
+ ··· + 12544y + 1024)
c
4
, c
5
, c
9
c
11
((y + 1)
4
)(y
34
+ 18y
33
+ ··· + 4y + 1)(y
58
+ 35y
57
+ ··· − 16y + 1)
c
7
((y
2
− y + 1)
2
)(y
29
− y
28
+ ··· + 31y −1)
2
· (y
34
− 3y
33
+ ··· + 563y + 36)
c
8
, c
10
((y −1)
4
)(y
34
+ 2y
33
+ ··· − 12y + 1)(y
58
− 25y
57
+ ··· − 84y + 1)
23
